Question

Q.3 For each of the following system of equations find whether it has unique solution, infinite number of solutions or no solutions

$3x-2y=8,5x-10y=7$

Answer 1

Step 1:Given Equations

Understanding & Applying

The given system of equation may be written as,

$3x-2y=8,5x-10y=7$

The given system of equations is of the form

$$\begin{gathered} a_{1}x+b_{1}y+c_1=0 \\ {a}_{2}x+b_{2}y+c_2=0 \end{gathered}$$

Step 2: Given values

$$\begin{gathered} Valuesof{a}_1,b_1,c_{1}and{a}_2,b_2,c_2 \\ where{a}_1=3,b_1=-2,c_1=-8 \\ {a}_2=5,b_2=-10,c_2=-7 \end{gathered}$$

Step 3:Equationg the coefficients of the given equation

We have

$\frac{a_1}{a_2}=\frac{3}{5},\frac{b_1}{b_2}=\frac{-2}{-10}=\frac{1}{5},\frac{c_1}{c_2}=\frac{-8}{-7}$

Step 4: Result

Clearly $$\begin{gathered} \frac{a_1}{a_2}isnotequalto\frac{b_1}{b_2} \\ \frac{3}{5}isnotequalto\frac{1}{5} \end{gathered}$$

Therefore The given system of equation has unique solution.